I've missed exams before and presented a doctors note within a few days of the exam. This way I could do the exam during repeats in August or whenever they're on for you and not have to pay or be penalized grades (our repeats where capped at 40% if you failed the first time). Surely they'll have a similar facility in your uni. I wouldn't worry about it, it'd probably be good to put it off until you're in a better head space. Good luck!